IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v18y1972i5-part-2p54-63.html
   My bibliography  Save this article

Some Thoughts on the Minimax Principle

Author

Listed:
  • R. J. Aumann

    (The Hebrew University of Jerusalem)

  • M. Maschler

    (The Hebrew University of Jerusalem)

Abstract

It is generally agreed that the minimax solution to a two-person zero-sum matrix game is intuitively satisfactory. Now in many applications of game theory, a game is not described a priori in matrix (or "normal" or "strategic") form, but rather in extensive form, i.e., by its rules. A game described in such a way may be reduced to a matrix game by means of the concept of "strategy." If, moreover, it is of perfect recall, then all mixed strategies, and in particular the optimal strategies of each player, are equivalent to behavior strategies. The usual conclusion from these considerations is that for 2-person 0-sum games in extensive form, the minimax solution is intuitively satisfactory; and that in games of perfect recall, in particular, the players would do well to play in accordance with optimal (minimax) behavior strategies. In this paper we shall discuss some examples that, we believe, cast doubt on these conclusions.

Suggested Citation

  • R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
  • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:5-part-2:p:54-63
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.18.5.54
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guillermo Owen, 2010. "Michael Maschler’s bibliography," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 301-308, March.
    2. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    3. Vitaly Pruzhansky, 2003. "Maximin Play in Two-Person Bimatrix Games," Tinbergen Institute Discussion Papers 03-101/1, Tinbergen Institute.
    4. Ismail M.S., 2014. "Maximin equilibrium," Research Memorandum 037, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Meir Pachter, 2017. "LQG Dynamic Games with a Control-Sharing Information Pattern," Dynamic Games and Applications, Springer, vol. 7(2), pages 289-322, June.
    6. Kaneko, Mamoru, 1982. "Some remarks on the folk theorem in game theory," Mathematical Social Sciences, Elsevier, vol. 3(3), pages 281-290, October.
    7. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, EconWPA, revised 18 Sep 1996.
    8. Robert W. Rosenthal, 1976. "An Arbitration Model for Normal-Form Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 82-88, February.
    9. Souza, Filipe & Rêgo, Leandro, 2012. "Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable," MPRA Paper 43408, University Library of Munich, Germany.
    10. Vitaly Pruzhansky, 2004. "A Discussion of Maximin," Tinbergen Institute Discussion Papers 04-028/1, Tinbergen Institute.
    11. Buechel, Berno & Emrich, Eike & Pohlkamp, Stefanie, 2013. "Nobody's innocent: the role of customers in the doping dilemma," MPRA Paper 44627, University Library of Munich, Germany.
    12. Gauer, Florian & Kuzmics, Christoph, 2016. "Cognitive empathy in conflict situations," Center for Mathematical Economics Working Papers 551, Center for Mathematical Economics, Bielefeld University.
    13. HHironori Otsubo, 2012. "Contests with Incumbency Advantages: An Experiment Investigation of the Effect of Limits on Spending Behavior and Outcome," Jena Economic Research Papers 2012-020, Friedrich-Schiller-University Jena.
    14. Rapoport, Amnon & Amaldoss, Wilfred, 2000. "Mixed strategies and iterative elimination of strongly dominated strategies: an experimental investigation of states of knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 483-521, August.
    15. Vitaly Pruzhansky, 2011. "Some interesting properties of maximin strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 351-365, May.
    16. Gregory B. Pollock & Antonio Cabrales, 1998. "Weak and strong altruism in traitgGroups: Reproductive suicide, personal fitness and expected value," Economics Working Papers 316, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Jason Shachat & J. Todd Swarthout & Lijia Wei, 2011. "Man versus Nash An experiment on the self-enforcing nature of mixed strategy equilibrium," Working Papers 1101, Xiamen Unversity, The Wang Yanan Institute for Studies in Economics, Finance and Economics Experimental Laboratory, revised 21 Feb 2011.
    18. Vitaly Pruzhansky, 2013. "Maximin play in completely mixed strategic games," Theory and Decision, Springer, vol. 75(4), pages 543-561, October.
    19. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, vol. 40(1), pages 123-146, July.
    20. Martin Shubik, 1988. "The Interaction of Implicit and Explicit Contracts in Repeated Agency," Cowles Foundation Discussion Papers 891, Cowles Foundation for Research in Economics, Yale University.
    21. repec:eee:gamebe:v:104:y:2017:i:c:p:666-673 is not listed on IDEAS

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:18:y:1972:i:5-part-2:p:54-63. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.